Classical and Quantum Parametric Phenomena
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Classical and Quantum Parametric Phenomena
Eichler, Alexander; Zilberberg, Oded
Oxford University Press
09/2023
192
Dura
Inglês
9780192862709
15 a 20 dias
Descrição não disponível.
Introduction
0.1: Historical Review
0.2: Present and Future
1 The Harmonic Resonator
1.1: Newton's Equation of Motion
1.2: Response of the Driven Resonator
1.3: Matrix Formulation
1.4: Parametric Modulation
1.5: Floquet Theory
1.6: Summary of Chapter 1
1.7: Exercises for Chapter 1
2 The Duffing Resonator
2.1: The Quartic Potential
2.2: The Cubic Potential
2.3: Summary of Chapter 2
2.4: Exercises for Chapter 2
3 Degenerate Parametric Pumping
3.1: The Nonlinear Parametric Resonator
3.2: Parametric Pumping via Three-Wave Mixing
3.3: Summary of Chapter 3
3.4: Exercises for Chapter 3
4 Dissipation and Force Fluctuations
4.1: The Role of Force Noise
4.2: The Fluctuation-Dissipation Theorem
4.3: The Probability Distribution Approach
4.4: Summary of Chapter 4
4.5: Exercises for Chapter 4
5 Parametric Resonators with Force Noise
5.1: Multistability and Quasi-Stable Solutions
5.2: Parametric Amplification Below Threshold
5.3: Parametric Pumping Above Threshold
5.4: Hierarchy of Relevant Timescales
5.5: Summary of Chapter 5
5.6: Exercises for Chapter 5
6 Coupled Harmonic Resonators
6.1: Static Coupling
6.2: Nondegenerate Three-Wave Mixing
6.3: Alternative Types of Coupling
6.4: Summary of Chapter 6
6.5: Exercises for Chapter 6
7 Coupled Parametric Oscillators
7.1: Equations for N Coupled Parametric Oscillators
7.2: Examples for N = 2
7.3: Networks with N > 2
7.4: Summary of Chapter 7
7.5: Exercises for Chapter 7
8 The Quantum Harmonic Oscillator
8.1: From Classical to Quantum Fluctuations
8.2: From First to Second Quantization
8.3: Quantum State Representations
8.4: Summary of Chapter 8
8.5: Exercises for Chapter 8
9 From Closed to Open Quantum Systems
9.1: Coupling to a Thermal Environment
9.2: The Driven Quantum Resonator
9.3: Summary of Chapter 9
9.4: Exercises for Chapter 9
10 The Quantum Parametric Oscillator
10.1: General Hamiltonian
10.2: Quantum Parametric Phenomena
10.3: Coupled Quantum Parametric Oscillators
10.4: Summary of Chapter 10
10.5: Exercises for Chapter 10
11 Experimental Systems
11.1: Mechanical Resonator Example
11.2: Electrical Resonator Example
11.3: Optical Resonator Example
11.4: Rescaling of the Numerical Values
11.5: Summary of Chapter 11
11.6: Exercises for Chapter 11
List of Important Symbols
0.1: Historical Review
0.2: Present and Future
1 The Harmonic Resonator
1.1: Newton's Equation of Motion
1.2: Response of the Driven Resonator
1.3: Matrix Formulation
1.4: Parametric Modulation
1.5: Floquet Theory
1.6: Summary of Chapter 1
1.7: Exercises for Chapter 1
2 The Duffing Resonator
2.1: The Quartic Potential
2.2: The Cubic Potential
2.3: Summary of Chapter 2
2.4: Exercises for Chapter 2
3 Degenerate Parametric Pumping
3.1: The Nonlinear Parametric Resonator
3.2: Parametric Pumping via Three-Wave Mixing
3.3: Summary of Chapter 3
3.4: Exercises for Chapter 3
4 Dissipation and Force Fluctuations
4.1: The Role of Force Noise
4.2: The Fluctuation-Dissipation Theorem
4.3: The Probability Distribution Approach
4.4: Summary of Chapter 4
4.5: Exercises for Chapter 4
5 Parametric Resonators with Force Noise
5.1: Multistability and Quasi-Stable Solutions
5.2: Parametric Amplification Below Threshold
5.3: Parametric Pumping Above Threshold
5.4: Hierarchy of Relevant Timescales
5.5: Summary of Chapter 5
5.6: Exercises for Chapter 5
6 Coupled Harmonic Resonators
6.1: Static Coupling
6.2: Nondegenerate Three-Wave Mixing
6.3: Alternative Types of Coupling
6.4: Summary of Chapter 6
6.5: Exercises for Chapter 6
7 Coupled Parametric Oscillators
7.1: Equations for N Coupled Parametric Oscillators
7.2: Examples for N = 2
7.3: Networks with N > 2
7.4: Summary of Chapter 7
7.5: Exercises for Chapter 7
8 The Quantum Harmonic Oscillator
8.1: From Classical to Quantum Fluctuations
8.2: From First to Second Quantization
8.3: Quantum State Representations
8.4: Summary of Chapter 8
8.5: Exercises for Chapter 8
9 From Closed to Open Quantum Systems
9.1: Coupling to a Thermal Environment
9.2: The Driven Quantum Resonator
9.3: Summary of Chapter 9
9.4: Exercises for Chapter 9
10 The Quantum Parametric Oscillator
10.1: General Hamiltonian
10.2: Quantum Parametric Phenomena
10.3: Coupled Quantum Parametric Oscillators
10.4: Summary of Chapter 10
10.5: Exercises for Chapter 10
11 Experimental Systems
11.1: Mechanical Resonator Example
11.2: Electrical Resonator Example
11.3: Optical Resonator Example
11.4: Rescaling of the Numerical Values
11.5: Summary of Chapter 11
11.6: Exercises for Chapter 11
List of Important Symbols
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Introduction
0.1: Historical Review
0.2: Present and Future
1 The Harmonic Resonator
1.1: Newton's Equation of Motion
1.2: Response of the Driven Resonator
1.3: Matrix Formulation
1.4: Parametric Modulation
1.5: Floquet Theory
1.6: Summary of Chapter 1
1.7: Exercises for Chapter 1
2 The Duffing Resonator
2.1: The Quartic Potential
2.2: The Cubic Potential
2.3: Summary of Chapter 2
2.4: Exercises for Chapter 2
3 Degenerate Parametric Pumping
3.1: The Nonlinear Parametric Resonator
3.2: Parametric Pumping via Three-Wave Mixing
3.3: Summary of Chapter 3
3.4: Exercises for Chapter 3
4 Dissipation and Force Fluctuations
4.1: The Role of Force Noise
4.2: The Fluctuation-Dissipation Theorem
4.3: The Probability Distribution Approach
4.4: Summary of Chapter 4
4.5: Exercises for Chapter 4
5 Parametric Resonators with Force Noise
5.1: Multistability and Quasi-Stable Solutions
5.2: Parametric Amplification Below Threshold
5.3: Parametric Pumping Above Threshold
5.4: Hierarchy of Relevant Timescales
5.5: Summary of Chapter 5
5.6: Exercises for Chapter 5
6 Coupled Harmonic Resonators
6.1: Static Coupling
6.2: Nondegenerate Three-Wave Mixing
6.3: Alternative Types of Coupling
6.4: Summary of Chapter 6
6.5: Exercises for Chapter 6
7 Coupled Parametric Oscillators
7.1: Equations for N Coupled Parametric Oscillators
7.2: Examples for N = 2
7.3: Networks with N > 2
7.4: Summary of Chapter 7
7.5: Exercises for Chapter 7
8 The Quantum Harmonic Oscillator
8.1: From Classical to Quantum Fluctuations
8.2: From First to Second Quantization
8.3: Quantum State Representations
8.4: Summary of Chapter 8
8.5: Exercises for Chapter 8
9 From Closed to Open Quantum Systems
9.1: Coupling to a Thermal Environment
9.2: The Driven Quantum Resonator
9.3: Summary of Chapter 9
9.4: Exercises for Chapter 9
10 The Quantum Parametric Oscillator
10.1: General Hamiltonian
10.2: Quantum Parametric Phenomena
10.3: Coupled Quantum Parametric Oscillators
10.4: Summary of Chapter 10
10.5: Exercises for Chapter 10
11 Experimental Systems
11.1: Mechanical Resonator Example
11.2: Electrical Resonator Example
11.3: Optical Resonator Example
11.4: Rescaling of the Numerical Values
11.5: Summary of Chapter 11
11.6: Exercises for Chapter 11
List of Important Symbols
0.1: Historical Review
0.2: Present and Future
1 The Harmonic Resonator
1.1: Newton's Equation of Motion
1.2: Response of the Driven Resonator
1.3: Matrix Formulation
1.4: Parametric Modulation
1.5: Floquet Theory
1.6: Summary of Chapter 1
1.7: Exercises for Chapter 1
2 The Duffing Resonator
2.1: The Quartic Potential
2.2: The Cubic Potential
2.3: Summary of Chapter 2
2.4: Exercises for Chapter 2
3 Degenerate Parametric Pumping
3.1: The Nonlinear Parametric Resonator
3.2: Parametric Pumping via Three-Wave Mixing
3.3: Summary of Chapter 3
3.4: Exercises for Chapter 3
4 Dissipation and Force Fluctuations
4.1: The Role of Force Noise
4.2: The Fluctuation-Dissipation Theorem
4.3: The Probability Distribution Approach
4.4: Summary of Chapter 4
4.5: Exercises for Chapter 4
5 Parametric Resonators with Force Noise
5.1: Multistability and Quasi-Stable Solutions
5.2: Parametric Amplification Below Threshold
5.3: Parametric Pumping Above Threshold
5.4: Hierarchy of Relevant Timescales
5.5: Summary of Chapter 5
5.6: Exercises for Chapter 5
6 Coupled Harmonic Resonators
6.1: Static Coupling
6.2: Nondegenerate Three-Wave Mixing
6.3: Alternative Types of Coupling
6.4: Summary of Chapter 6
6.5: Exercises for Chapter 6
7 Coupled Parametric Oscillators
7.1: Equations for N Coupled Parametric Oscillators
7.2: Examples for N = 2
7.3: Networks with N > 2
7.4: Summary of Chapter 7
7.5: Exercises for Chapter 7
8 The Quantum Harmonic Oscillator
8.1: From Classical to Quantum Fluctuations
8.2: From First to Second Quantization
8.3: Quantum State Representations
8.4: Summary of Chapter 8
8.5: Exercises for Chapter 8
9 From Closed to Open Quantum Systems
9.1: Coupling to a Thermal Environment
9.2: The Driven Quantum Resonator
9.3: Summary of Chapter 9
9.4: Exercises for Chapter 9
10 The Quantum Parametric Oscillator
10.1: General Hamiltonian
10.2: Quantum Parametric Phenomena
10.3: Coupled Quantum Parametric Oscillators
10.4: Summary of Chapter 10
10.5: Exercises for Chapter 10
11 Experimental Systems
11.1: Mechanical Resonator Example
11.2: Electrical Resonator Example
11.3: Optical Resonator Example
11.4: Rescaling of the Numerical Values
11.5: Summary of Chapter 11
11.6: Exercises for Chapter 11
List of Important Symbols
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